Question

What is the resistance of a 1.3-m-long copper wire that is 0.30 mm in diameter?

Answer 1

The resistance R of a wire is given by:

`R= (\rho L)/(A)`
where

`\rho` is the resistivity of the material
L is the length of the wire
A is the cross-sectional area of the wire.

For the wire in the problem, the resistivity is (copper resistivity)
`\rho=1.68 \cdot 10^(-8) \Omega m`. The length of the wire is L=1.3 m, while the cross-sectional area is

`A=\pi r^2 = \pi ( (d)/(2))^2 = \pi ( (0.30 \cdot 10^(-3) m)/(2) )^2 =7.07 \cdot 10^(-8) m^2`

so the resistance of the wire is:

`R= ((1.68 \cdot 10^(-8) \Omega m)(1.3 m))/(7.07 \cdot 10^(-8) m^2)=0.31 \Omega`